Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm

Federica Milinanni; Pierre Nyquist

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arXiv · 2403.08691

Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm

Federica Milinanni·Pierre Nyquist

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Abstract

In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation results for empirical measures of Markov chains arising from specific Metropolis-Hastings methods on a continuous state space. Moreover, we show that the existing large deviation framework, that we developed in a previous work (Milinanni and Nyquist, 2024), does not cover the Random Walk Metropolis sampler, even in cases when the underlying Markov chain is geometrically ergodic.

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BibTeX RIS

Federica Milinanni, Pierre Nyquist. 2024-03-13. Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm. https://arxiv.org/abs/2403.08691

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